A classical Cepheid variable star is seen to vary regularly with a period of 25 days.How many times brighter than the Sun would this star appear to be if it were to replace the Sun in our solar system? (See Figure 13-3 of Comins,Discovering the Essential Universe,6th ed.)
A) 1000
B) 4
C) 10,000
D) 10²

Question

Quizplus · Accepted Answer

The period-luminosity relation for Cepheid variable stars tells us that the brightness of the star is related to its period of variability. Specifically, brighter Cepheids have longer periods.

Assuming this Cepheid variable star has the same luminosity as the Sun, we can use the period-luminosity relation to determine how much brighter it appears compared to the Sun. According to Figure 13-3 in the textbook, a Cepheid variable with a period of 25 days is about 10,000 times more luminous than the Sun.

The apparent brightness of a star is proportional to its luminosity divided by the square of its distance from us. If this Cepheid variable were to replace the Sun in our solar system, its distance from us would be 1 astronomical unit (AU), the same as the Sun's distance from us. Therefore, the Cepheid variable would appear 10,000 times brighter than the Sun.

Answer: C.

A Classical Cepheid Variable Star Is Seen to Vary Regularly